Simultaneous effect of hydrostatic pressure and polaronic mass on the binding energies of the ground and excited states of an on-center hydrogenic impurity confined in a GaAs/GaAlAs spherical quantum dot are theoretically investigated by the variational method within the effective mass approximation. The binding energy is calculated as a function of dot radius and pressure. Our findings proved that the hydrostatic pressure led to the decrease of confined energy and the increase of donor binding energy. Conduction band non-parabolicity and the polaron masses are effective in the donor binding energy which is significant for narrow dots not in the confined energy. The maximum donor binding energy achieved by the polaronic mass in the ground and excited states are 2%–19%for the narrow dots. The confined and donor binding energies approach zero as the dot size approaches infinity.